A Dynamics Problem Regarding Friction.

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AI Thread Summary
The discussion revolves around a dynamics problem involving friction and the motion of two stacked masses. The user successfully calculated the coefficient of static friction for the bottom mass but is struggling with determining the time it takes for the top mass to fall off after it starts sliding. Initial calculations yielded an incorrect time of 0.82 seconds, prompting a reevaluation of the acceleration needed relative to the bottom block. Clarification is sought on whether to consider the top block's movement relative to the bottom block, which is essential for solving part c of the problem. The conversation highlights the importance of understanding relative motion in dynamics problems.
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Homework Statement



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That was the given information. Here are the questions they ask, I have solved a) and b), but I am completely stuck on c). I'll just put them here in case information from them are necessary.

a) What is the coefficient of static friction between the 5.0 kg mass and the horizontal surface? (answer 0.33)

b) What is the coefficient of static friction between the two masses?

c) From the point when the top mass starts sliding how long will it take for the top mass to fall off the bottom mass? (0.97s)

Homework Equations



F=ma
fric = μ|Fn|

The Attempt at a Solution



Block on Top (2.0kg)
ƩFx=-fk
ƩFx=-(0.3)(2kg*9.81m/s^2)
ma=-(0.3)(2kg*9.81m/s^2)
2kg*a=-5.886N
a= \frac{-5.886N}{2kg}
a= -2.943m/s^2

then...
Δd=viΔt+\frac{1}{2}aΔt^2
-1m=\frac{1}{2}2.943m/s^2*Δt^2
-1m=-1.4715m/s^2*Δt^2
-1m=-1.4715m/s^2*Δt^2
\frac{-2m}{-1.4715m/s^2}=Δt^2
Δt^2=0.68s^2
Δt=0.82s^Which is wrong =(
 
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You've found the 2kg's acceleration relative to the ground (except, not sure why you have it as negative; isn't positive to the right?). Is that the acceleration you need to answer the question?
 
So does that mean I need to find the acceleration relative to the bottom block?
 
AvocadosNumber said:
So does that mean I need to find the acceleration relative to the bottom block?
You want the time it takes the top block to move 1m, starting from 'rest'. 1m relative to what? "rest" relative to what?
 
Oh... I see now... relative to the bottom block.
 
Quite so.
 
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